From experience I can say that things can and do get nasty, for two main reasons. One, you are threatening someone's money. Two, face, you are calling someone out for not doing their job. @faber mentions "sought out by the opposition for pacification in private."
As a foreigner you are a soft target, and any accusations (true or false) could be levelled at you, just out of vexation. Let someone else take that heat. Yes ask around, and maybe encourage someone else to take a lead, but then step back. If anyone asks why you are not taking a lead, just say that you are a foreigner and not allowed to (this may or may not be a true fact).
I do know that there is a legal vehicle for setting up owners associations and regulations that govern this. I am not sure if this is the same as a Street Committee (the grass roots level of the CCP in urban areas), but there is a mechanism for setting up a local street committee. If your street does not have one, these branches of the CCP can be found at local or district levels, and they can advise. Even if your 'street' does have one, your local area can form their own, it takes very few people. I know that any eligible group is allowed to form one, and it is encouraged by CCP policy. In either of these cases (owners assoc. or street ctte.) I think foreigners would not be eligible.
@livinginchina, do you meet the criteria for the permanent residence card? If you do it might be worth applying. Permanent residence cards are actually attainable for mere mortals now, you don't need to be a captain of industry, diplomat, or research professor anymore.
@Pete B. Looking at what @fabey posted. It would probably help to have on hand a copy of any documentation to show that you will be resident.
If it is for a job, get your employer to scan and email a letter to this effect, with an address where you will live (if that has been organized).
If for family reunion, get the family to scan email you a copy of the household ID, rental agreement, of the address where you will live. As well as a signed letter saying you will be living there, and a scan copy of the ID card of the person signing the letter.
You may not need these, and I am not saying that this will do the job, but it will go a long way to help baffling the bureaucrats into submission if they do start dithering.
In the past, I have heard of people being denied renewal if they left it to the last week. Since then I have usually applied 3 weeks before expiry, and it has usually taken two weeks to get the new visa.
At the moment things are quiet and processing time may well be a bit shorter, but I wouldn't risk it if I didn't have to. If I remember correctly the new visa was dated for one calendar year beyond the expiry date of the old visa, I didn't lose the weeks worth of cover. However, this was for a renewal at the appointed time, not an early renewal, as in the case in the above post. The last time I applied was May 2021.